Well if you want, I can't imagine anyone will stop you. However, I think that this dress would be a little too fancy for class. People might stare, point, or ask a lot of questions. Then there's questions about comfort, or whether or not you're sure you can keep it clean all day. So yeah this might not be advised. Still yeah you could wear it.
I say you can probably wear it, no problem. You do look nice, just remember that there are all the other things I mentioned above to consider. So keep it in mind. Barring that... do whatever the hell you want and wear whatever you want.